163
in shape memory alloys is considered and it is again seen that a thermodynamically consistent constitutive modeling of the referential velocity of sharp interfaces is not at all straight forward. This again motivates the use of a phase field approach.
Based on these considerations, we propose anew phase field model for the formation and evolution of laminate microstructure between two orthorhombic variants of CuAlNi in the modeling framework of gradient-extended standard-dissipative solids, see also Hilde-brand & Miehe[71, 72]. The model is based on the variational smooth approximation of sharp interfaces. In contrast to sharp interface models, this smooth approximation allows the introduction of a coherence-dependent interface energy by use of a referential anisotropy. A bulk energy is proposed that is based on aninternal mixing approach, al-lowing a bulk energy free connection of the rank-one connected minima and hence leading to aclear separation of bulk and interface energy. A viscous evolution yields a generalized Ginzburg-Landau model, for which we construct rate- and incremental variational formu-lations as well as a variational-based finite element formulation with symmetric algebraic structure. We validate the energetic modeling properties of the proposed formulation and confirm the superiority of the internal mixing approach over the external mixing approach for the bulk energy. We demonstrate the capability of the model to predict theformation and hysteretic evolution of laminate microstructure and the description ofsize effects.
Finally, to model the formation and evolution of laminate deformation microstructure together with the effect of geometrically necessary dislocations in f.c.c. Copper with two active slip systems on the same slip plane in the modeling framework of gradient-extended standard-dissipative solids, we propose a new gradient crystal plasticity model, see also Miehe et al. [113] and Hildebrand & Miehe [73]. Based on the assumption of same plane double slip, we derive explicit expressions for the plastic deformation and the dislocation density tensor. We introduce accumulated slips whose evolution we compute using a new rate regularized evolution based on the approximation|x| ≈νln(cosh(x/ν)) for ν ≪ 1 and employ them to define a biquadratic latent hardening contribution of a qualitatively physical nonconvex form. We combine this with a gradient contribution in the slip normal direction to regularize the resulting sharp slip state laminate interfaces and introduce an additional gradient contribution directly constructed from the dislocation density tensor to account for GNDs. In combination, these gradient terms lead to a reference anisotropy of the gradient energy contribution. The evolution equations of the plastic slips are given in terms of rate regularizations of the dissipation potential again by use of the ln(cosh(x)) function. We demonstrate the capability of the presented model to predict the formation and evolution of plastic laminates under micro-free and micro-clamped boundary conditions in combination with length scale effects caused by geometrically necessary dislocations.
From the two models, we deduce that necessary ingredients for the energetically concise gradient-extended modeling of laminate microstructure are:
• non-convexity of the free energy in terms of the internal variables,
• rank-one connection of deformations associated with internal variable minimizers,
• bulk energy free connection of these rank-one connected deformation states,
• anisotropic gradient term favoring the direction of the the rank-one normal.
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Curriculum Vitae
Personal Data
Name Felix Eberhard Hildebrand
Date of Birth November 20, 1979 Place of Birth T¨ubingen a.N., Germany
School Education/Community Service
1986–1987 Elementary school “Grundschule Hofen”, Stuttgart 1987–1990 Elementary school “Wilhelm-Hauff Schule”, Stuttgart 1990–1992 High school “Karlsgymnasium”, Stuttgart
1992–1999 High school “Beethovengymnasium”, Bonn
1996–1997 Maple Ridge Secondary School, Vancouver, Canada 1999–2000 Community Service “Jugendcolloquium e.V.”, Bonn
University Education
2000–2003 Pre-Diploma Studies in Mechanical Engineering, Technical University of Berlin
2003–2004 Master of Science in Mechanical Engineering, University of Michigan, Ann Arbor, USA 2004–2006 Diploma studies in Engineering Science,
Technical University of Berlin
2005–2006 Master thesis at the Department of Mechanical Engineering, Massachusetts Institute of Technology, Boston, USA
Professional Occupation
2006–2009 Research Associate at the Center of Mechanics,
Swiss Federal Institute of Technology, Zurich, Switzerland 2009–2013 Research Associate and Assistant Lecturer at the
Institute of Applied Mechanics (CE), University of Stuttgart
In dieser Schriftenreihe bisher erschienene Berichte:
I-1(1996) Theoretische und algorithmische Konzepte zur ph¨anomenologischen Beschrei-bung anisotropen Materialverhaltens, J. Schr¨oder, Dissertation, 1996.
I-2(1996) Zur Theorie und Numerik finiter elastoplastischer Deformationen von Scha-lentragwerken, B. Seifert, Dissertation, 1996.
I-3(1996) Zur Modellierung des k¨unstlichen Infrarot-Dichroismus in Poymerfolien bei großen Verformungen, J. Buhler, Dissertation, 1996.
I-4(1998) Verfahren zur Ermittlung der Erdbebenlasten mit Ber¨ucksichtigung des stochastischen Charakters des Bebens, S. Zhang, Dissertation, 1998.
I-5(1998) Zur Beschreibung finiter Deformationen von Polymeren: Experimente, Mod-ellbildung, Parameteridentikation und Finite-Elemente- Formulierung, J.
Keck, Dissertation, 1998.
I-6(1999) Berechnungsverfahren instation¨ar erregter Systeme im Frequenzbereich, A.
Jaworek, Dissertation, 1999.
I-7(2000) Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Stabilit¨atsproblemen, J. Schr¨oder, Habilitation, 2000.
I-8(2002) Theorie und Numerik von Materialinst¨abilitaten elastoplastischer Festk¨orper auf der Grundlage inkrementeller Variationsformulierungen, M. Lambrecht, Dissertation, 2002.
I-9(2002) Mikromechanisch motivierte Modelle zur Beschreibung finiter Deformationen gummiartiger Polymere: physikalische Modellbildung und numerische Simu-lation, F. Lulei, Dissertation, 2002.
I-10(2003) Adaptive Finite-Elemente-Berechnungen der nichtlinearen Festk¨orper-mechanik bei kleinen und großen Verzerrungen, A. Koch, Dissertation, 2003.
I-11(2003) Theorie und Numerik der Parameteridentikation von Materialmodellen der finiten Elastizit¨at und Inelastizit¨at auf der Grundlage optischer Feld-meßmethoden, G. Scheday, Dissertation, 2003.
I-12(2004) Approaches to the Description of Anisotropic Material Behaviour at Finite Elastic and Plastic Deformations, Theory and Numerics, N. Apel, Disserta-tion, 2004.
I-13(2004) Temperaturabh¨angige Beschreibung visko-elasto-plastischer Deformationen kurzglasfaserverst¨arkter Thermoplaste: Modellbildung, Numerik und Experi-mente, S. Rieger, Dissertation, 2004.
I-14(2005) Zur Parameteridentikation komplexer Materialmodelle auf der Basis realer und virtueller Testdaten, A. Rieger, Dissertation, 2005.
I-15(2005) Viskoelastisches Verhalten von Elastomeren bei finiten Verzerrungen: Exper-imente, Modellierung und Simulationen, H. Zecha, Dissertation, 2005.
2005.
I-17(2005) Static and Dynamic Homogenization Analyses of Discrete Granular and Atomistic Structures on Different Time and Length Scales, J. Dettmar, Dis-sertation, 2005.
I-18(2006) Incompatibility and Instability Based Size Effects in Crystals and Composites at Finite Elastoplastic Strains, M. Becker, Dissertation, 2006.
I-19(2007) Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation, E. G¨urses, Dissertation, 2007.
I-20(2007) Micro-Macro Approaches to Rubbery and Glassy Polymers: Predictive Micromechanically-Based Models and Simulations, S. G¨oktepe, Dissertation, 2007.
I-21(2008) Material Forces in Finite Inelasticity and Structural Dynamics: Topology Optimization, Mesh Refinement and Fracture, D. Zimmermann, Dissertation, 2008.
I-22(2010) Thermoviscoplasticity of Glassy Polymers: Experimental Characterization, Parameter Identification and Model Validation, J. M´endez Diez, Dissertation, 2010.
I-23(2010) On the Formulation and Numerical Implementation of Dissipative Electro–
Mechanics at Large Strains, D. Rosato, Dissertation, 2010.
I-24(2011) A Variational Framework for Gradient-Extended Dissipative Continua. Ap-plication to Damage Mechanics, Fracture, and Plasticity, F. Welschinger, Dissertation, 2011.
I-25(2013) Variational Multifield Modeling of the Formation and Evolution of Laminate Microstructure, F. Hildebrand, Dissertation, 2013.
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